Question: Multiply the following complex numbers: $({1+i}) \cdot ({3+5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1+i}) \cdot ({3+5i}) = $ $ ({1} \cdot {3}) + ({1} \cdot {5}i) + ({1}i \cdot {3}) + ({1}i \cdot {5}i) $ Then simplify the terms: $ (3) + (5i) + (3i) + (5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (5 + 3)i + 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 3 + (5 + 3)i - 5 $ The result is simplified: $ (3 - 5) + (8i) = -2+8i $